GRASP and path relinking for the matrix bandwidth minimization

Piñana, Estefanía; Plana, Isaac; Campos, Vicente; Martı́, Rafael

doi:10.1016/s0377-2217(02)00715-4

Cited by 84 publications

(62 citation statements)

References 14 publications

(13 reference statements)

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“…This is an extension of the move value definition introduced in Piñana et al (2004) which differs from the move value proposed in Martí et al (2001). In addition, we modified this evaluation which takes the value -K (the penalization K being a huge number) when the application of the move leads to a bandwidth of the vertex v, B f' (v) which is larger than the current bandwidth of the graph B f (G).…”

Section: Short-term Memorymentioning

confidence: 99%

“…Martí et al (2001) propose a TS method for this problem, which is likewise based on swap moves that exchange the labels of a pair of vertices; however, it incorporates memory structures that prove to be remarkably effective. Piñana et al (2004) proposed a GRASP method for the MBMP. The constructive step is based on GPS and the local search is based on exchanges.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive memory programming for matrix bandwidth minimization

2009

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In this paper we explore the influence of adaptive memory in the performance of heuristic methods when solving a hard combinatorial optimization problem. Specifically, we tackle the adaptation of tabu search and scatter search to the bandwidth minimization problem. It consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This is a classic problem, introduced in the late sixties, that also has a well-known formulation in terms of graphs. Different exact and heuristic approaches have been proposed for the bandwidth problem. Our contribution consists of two new algorithms, one based on the tabu search methodology and the other based on the scatter search framework. We also present a hybrid method combining both for improved outcomes. Extensive computational testing shows the influence of the different elements in heuristic search, such as neighbourhood definition, local search, combination methods and the use of memory. We compare our proposals with the most recent and advanced methods for this problem, concluding that our new methods can compete with them in speed and running time.

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Section: Short-term Memorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive memory programming for matrix bandwidth minimization

2009

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“…As far as we know, the GRASP algorithm by Piñana et al (2004) provides the best heuristic solution for this problem. We therefore use this solution as the initial upper bound of our branch and bound procedure.…”

Section: A New Branch and Bound Algorithmmentioning

confidence: 99%

“…Consider the following formulation, introduced in Piñana et al (2004) in which x ij =1 if label j is assigned to vertex i, and 0 otherwise. If we solve its relaxation (replacing (5) constraints with 0≤ x ij ≤1) in the example given in Figure 1, we would obtain the solution x ij =1/7 for all i and j with a value b=0.…”

Section: It Is Obvious Thatmentioning

confidence: 99%

“…For many years researchers were only interested in designing relatively simple heuristic procedures and sacrificed solution quality for speed (see for example Cuthill andMcKee 1969, or Gibbs, Poole andStockmeyer 1976). Recently, metaheuristics such as tabu search (Martí et al 2001) or GRASP (Piñana et al 2004), have been developed for this problem in order to obtain high quality solutions. The second line of research consists of the development of theoretical results (mainly lower bounds) and exact methods for the MBMP.…”

Section: Introductionmentioning

confidence: 99%

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A branch and bound algorithm for the matrix bandwidth minimization

Martı́

Campos

Piñana

2008

European Journal of Operational Research

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-In this article we first review previous exact approaches as well as theoretical contributions for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the non-zero elements of the corresponding symmetrical matrix. We propose a new branch and bound algorithm and new expressions for known lower bounds for this problem.Empirical results with a collection of previously reported instances indicate that the proposed algorithm compares favourably to previous methods.

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Accelerating unstructured finite volume computations on field‐programmable gate arrays

Nagy

Nemes

Hiba

et al. 2013

Concurrency and Computation

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SUMMARYIn the paper, an field‐programmable gate array (FPGA)‐based framework is described to efficiently accelerate unstructured finite volume computations where the same mathematical expression has to be evaluated at every point of the mesh. The irregular memory access patterns caused by the unstructured spatial discretization are eliminated by a novel mesh node reordering technique, and a special architecture is designed to fully utilize the benefits of the predictable memory access patterns. In the proposed architecture, a fixed‐size moving window of the input stream of the reordered state variables is cached into the on‐chip memory and a pipelined chain of processing elements, which gets input only from the fast on‐chip memory, is used to carry out the computations. The arithmetic unit (AU) of the processing elements is generated from the data flow graph extracted from the given mathematical expression. The data flow graph is partitioned with a novel graph partitioning algorithm to break up the AU into smaller locally controlled parts, which can be more efficiently implemented in FPGA than the globally controlled AU. The proposed architecture and algorithms are presented via a case study solving the Euler equations on an unstructured mesh. On the currently available largest FPGA, the generated architecture contains three processing elements working in a pipelined fashion to provide one order of magnitude speedup compared with a high performance microprocessor and three times speedup compared with a high performance graphics processing unit. Copyright © 2013 John Wiley & Sons, Ltd.

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GRASP and path relinking for the matrix bandwidth minimization

Cited by 84 publications

References 14 publications

Adaptive memory programming for matrix bandwidth minimization

Adaptive memory programming for matrix bandwidth minimization

A branch and bound algorithm for the matrix bandwidth minimization

Accelerating unstructured finite volume computations on field‐programmable gate arrays

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